A pure monopoly is characterized by a single seller of a unique product without close substitutes, the ability to set any price, and barriers to entry that prevent competition. While pure monopolies are rare, monopolies can exist when a firm is the only producer of a product and uses barriers like patents, large size, or unfair tactics to prevent competition. A monopoly has power over price as the sole provider of a product and sets price at the level that maximizes profits by balancing marginal revenue and marginal costs.